Determining profile parameters of a structure using approximation and fine diffraction models in optical metrology

ABSTRACT

Provided is a method for determining one or more profile parameters of a structure using an optical metrology model, the optical metrology model comprising a profile model, an approximation diffraction model, and a fine diffraction model. A simulated approximation diffraction signal is generated based on an approximation diffraction model of the structure. A set of difference diffraction signals is obtained by subtracting the simulated approximation diffraction signal from each of simulated fine diffraction signals and paired with the corresponding profile parameters. A machine learning system is trained using the pairs of difference diffraction signal and corresponding profile parameters. A measured diffraction signal adjusted by the simulated approximation diffraction signal is input into the trained machine learning system and generates the corresponding profile parameters.

BACKGROUND

1. Field

The present application generally relates to optical metrology of astructure formed on a semiconductor wafer, and, more particularly, todetermining one or more profile parameters of a structure usingapproximation and fine models in optical metrology.

2. Related Art

In semiconductor manufacturing, periodic gratings are typically used forquality assurance. For example, one typical use of periodic gratingsincludes fabricating a periodic grating in proximity to the operatingstructure of a semiconductor chip. The periodic grating is thenilluminated with electromagnetic radiation. The electromagneticradiation that deflects off of the periodic grating is collected as adiffraction signal. The diffraction signal is then analyzed to determinewhether the periodic grating, and by extension whether the operatingstructure of the semiconductor chip, has been fabricated according tospecifications.

In one conventional system, the diffraction signal collected fromilluminating the periodic grating (the measured diffraction signal) iscompared to a library of simulated diffraction signals. Each simulateddiffraction signal in the library is associated with a hypotheticalprofile. When a match is made between the measured diffraction signaland one of the simulated diffraction signals in the library, thehypothetical profile associated with the simulated diffraction signal ispresumed to represent the actual profile of the periodic grating.

Hypothetical profiles, which are used to generate simulated diffractionsignals, are generated based on a profile model that characterizes thestructure to be examined. Thus, in order to accurately determine theprofile of the structure using optical metrology, a profile model thataccurately characterizes the structure should be used.

SUMMARY

Provided is a method for determining one or more profile parameters of astructure using an optical metrology model, the optical metrology modelcomprising a profile model, an approximation diffraction model, and afine diffraction model. A simulated approximation diffraction signal isgenerated based on an approximation diffraction model of the structure.A set of difference diffraction signals is obtained by subtracting thesimulated approximation diffraction signals from each of simulated finediffraction signals and paired with the corresponding profile parametersand used to generate a library of difference diffraction signals. Ameasured diffraction signal adjusted by the simulated approximationdiffraction signal is matched against the library to determine at leastone profile parameter of the structure.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1A is an architectural diagram illustrating an exemplary embodimentwhere optical metrology can be utilized to determine the profiles ofstructures formed on a semiconductor wafer.

FIG. 1B depicts an exemplary one-dimensional repeating structure.

FIG. 1C depicts an exemplary two-dimensional repeating structure

FIG. 2A depicts an exemplary orthogonal grid of unit cells of atwo-dimensional repeating structure.

FIG. 2B depicts a top-view of a two-dimensional repeating structure.

FIG. 2C is an exemplary technique for characterizing the top-view of atwo-dimensional repeating structure.

FIG. 3A is an exemplary architectural diagram of two layers of materialdepicting a substrate and a metal film layer.

FIG. 3B is an exemplary architectural diagram of two layers of materialdepicting a substrate and a homogenous metal film layer.

FIG. 4A is an exemplary architectural diagram of an approximation modeldepicting an unpatterned film stack on a substrate.

FIG. 4B is an exemplary architectural diagram of a fine model depictinga patterned structure in the top layer of the thin film stack.

FIG. 5A is an exemplary architectural diagram of an approximation modeldepicting a stack of thin films on a substrate.

FIG. 5B is an exemplary side-view architectural diagram depicting astack of thin films with contact holes.

FIG. 5C is an exemplary top-view architectural diagram depicting a stackof thin films with contact holes.

FIG. 6A is an exemplary chart of a simulated fine diffraction signalusing a fine diffraction model versus a simulated approximationdiffraction signal using an approximation diffraction model of thestructure.

FIG. 6B is an exemplary chart of a calculated difference diffractionsignal.

FIG. 7A is an exemplary flowchart for determining profile parametersutilizing approximation and fine diffraction models.

FIG. 7B is an exemplary flowchart for determining profile parametersutilizing approximation and fine diffraction models using a first and asecond machine learning systems.

FIG. 7C is an exemplary flowchart for determining profile parametersutilizing approximation and fine diffraction models using one or moretermination criteria for metrology model optimization.

FIG. 8 is an exemplary block diagram of a system for utilizing a librarydeveloped for determining the profile parameters of a structure usingapproximation and fine diffraction models.

FIG. 9 is an exemplary block diagram of a system for utilizing a machinelearning system developed for determining the profile parameters of astructure using approximation and fine diffraction models.

FIG. 10 is an exemplary flowchart for determining and utilizing profileparameters using approximation and fine diffraction models for automatedprocess and equipment control.

FIG. 11 is an exemplary block diagram for determining and utilizingprofile parameters for automated process and equipment control.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENT(S)

In order to facilitate the description of the present invention, asemiconductor wafer may be utilized to illustrate an application of theconcept. The methods and processes equally apply to other work piecesthat have repeating structures. Furthermore, in this application, theterm structure when it is not qualified refers to a patterned structure.

FIG. 1A is an architectural diagram illustrating an exemplary embodimentwhere optical metrology can be utilized to determine the profiles orshapes of structures fabricated on a semiconductor wafer. The opticalmetrology system 40 includes a metrology beam source 41 projecting ametrology beam 43 at the target structure 59 of a wafer 47. Themetrology beam 43 is projected at an incidence angle θ towards thetarget structure 59. The diffracted beam 49 is measured by a metrologybeam receiver 51. The measured diffraction signal 57 is transmitted to aprofile server 53. The profile server 53 compares the measureddiffraction signal 57 against simulated diffraction signals and theirassociated hypothetical profiles representing various combinations ofdimensions of the target structure, simulated by and/or stored insimulator 60. The simulator 60 can be either a library that consists ofa machine learning system, a pre-generated simulated diffraction signaldatabase, or similar system (e.g. this is library method).Alternatively, it can be an on-demand diffraction signal generator thatsolves Maxwell's equations for a given profile (e.g. this is theregression method). In an exemplary embodiment, a diffraction signalgenerated by simulator 60 that best matches the measured diffractionsignal 57, is selected. The hypothetical profile and associateddimensions corresponding to the selected simulated diffraction signalare assumed to correspond to the actual profile and dimensions of thefeatures of target structure 59. The optical metrology system 40 mayutilize a reflectometer, scatterometer, ellipsometer, or other opticalmetrology device to measure the diffraction beam or signal. An opticalmetrology system is described in U.S. Pat. No. 6,943,900, entitledGENERATION OF A LIBRARY OF PERIODIC GRATING DIFFRACTION SIGNAL, issuedon Sep. 13, 2005, which is incorporated herein by reference in itsentirety.

Simulated diffraction signals can be generated by solving Maxwell'sequations using some numerical analysis technique. Various numericalanalysis techniques, including variations of rigorous coupled waveanalysis (RCWA) can be used. For a more detailed description of RCWA,see U.S. Pat. No. 6,891,626, titled CACHING OF INTRA-LAYER CALCULATIONSFOR RAPID RIGOROUS COUPLED-WAVE ANALYSES, filed on Jan. 25, 2001, issuedMay 10, 2005, which is incorporated herein by reference in its entirety.

Simulated diffraction signals can also be generated using a machinelearning system (MLS). Prior to generating the simulated diffractionsignals, the MLS is trained using known input and output data. In oneexemplary embodiment, simulated diffraction signals can be generatedusing an MLS employing a machine learning algorithm, such asback-propagation, radial basis function, support vector machine, kernelregression, and the like. For a more detailed description of machinelearning systems and algorithms as applied to optical metrology, seeU.S. patent application Ser. No. 10/608,300, titled OPTICAL METROLOGY OFSTRUCTURES FORMED ON SEMICONDUCTOR WAFERS USING MACHINE LEARNINGSYSTEMS, filed on Jun. 27, 2003, which is incorporated herein byreference in its entirety.

The term “one-dimensional structure” is used herein to refer to astructure having a profile that varies in one dimension. For example,FIG. 1B depicts a periodic grating having a profile that varies in onedimension (i.e., the x-direction). The profile of the periodic gratingdepicted in FIG. 1B is assumed to be substantially uniform or continuousin the y-direction.

The term “two-dimensional structure” is used herein to refer to astructure having a profile that varies in two-dimensions. For example,FIG. 1C depicts a periodic grating having a profile that varies in twodimensions (i.e., the x-direction and the y-direction).

FIGS. 2A, 2B, and 2C describe the characterization of two-dimensionalrepeating structures for optical metrology modeling. FIG. 2A depicts atop-view of an exemplary orthogonal grid of unit cells of atwo-dimensional repeating structure 300. A hypothetical grid of lines issuperimposed on the top-view of the repeating structure where the linesof the grid are drawn along the directions of periodicity. Thehypothetical grid of lines forms areas referred to as unit cells 302.The unit cells may be arranged in an orthogonal or non-orthogonalconfiguration. Two-dimensional repeating structures may comprisefeatures such as repeating posts, contact holes, vias, islands, orcombinations of two or more shapes within a unit cell. Furthermore, thefeatures may have a variety of shapes and may be concave or convexfeatures or a combination of concave and convex features. Referring toFIG. 2A, the repeating structure 300 comprises unit cells 302 with holes304 arranged in an orthogonal manner, wherein holes 304 are locatedsubstantially at the centers of unit cells 302.

FIG. 2B depicts a top-view of a two-dimensional repeating structure unitcell 310, which includes a concave elliptical hole 320. The dimensionsof hole 320 become progressively smaller until the bottom of the hole.Profile parameters used to characterize the structure include theX-pitch 310 and the Y-pitch 314. In addition, the major axis of theellipse 316 at the top of the hole 320 and the major axis of the ellipse318 at the bottom of hole 320 may be used to characterize the hole 320.Furthermore, any intermediate major axis between the top and bottom ofthe hole may also be used as well, as also any minor axis (not shown).

FIG. 2C shows an exemplary technique for characterizing the top-view ofa two-dimensional repeating structure. Unit cell 330 includes a feature332, which is an island with a peanut shape viewed from the top. Onemodeling approach includes approximating the feature 332 with acombination of ellipses and polygons. Assuming further that afteranalyzing the production variability of the top-view shape of thefeature 332, it has been determined that two ellipses, ellipse 1 andellipse 2, and two polygons, polygon 1 and polygon 2, may be used tofully characterize feature 332. In turn, parameters needed tocharacterize the two ellipses and two polygons comprise nine parametersas follows: major and minor axes T1 and T2 for ellipse 1; dimensions T3and T4, and angle θ₁ for polygon 1; dimensions T4 and T5, and angle θ₂for polygon 2; and major and minor axes T6 and T7 for ellipsoid 2. Manyother combinations of shapes could be used to characterize the top-viewof feature 332 inside unit cell 330. For a detailed description ofmodeling two-dimensional repeating structures, refer to U.S. patentapplication Ser. No. 11/061,303, OPTICAL METROLOGY OPTIMIZATION FORREPETITIVE STRUCTURES, filed on Apr. 27, 2004, which is incorporatedherein by reference in its entirety.

FIG. 3A is an exemplary architectural diagram of a structure 400comprising a substrate 404 and a metal film layer 402. The metal filmlayer 402 is inhomogeneous as a result of irregularities of thedeposition process. FIG. 3B is an exemplary architectural diagram ofstructure 410 comprising a substrate 414 and a homogenous metal filmlayer 412. In general, if the two structures, 400 and 410, depicted inFIGS. 3A and 3B are measured using an optical metrology device such as areflectometer or ellipsometer (not shown); they will produce differentdiffraction signals. However, if the sizes of the individualirregularities in the inhomogeneous metal film layer 402 are muchsmaller than the wavelength of the incident light beam of the opticalmetrology device, the inhomogeneous metal film layer 402 can be treatedas a macroscopically homogenous medium. Optical properties of theinhomogeneous metal film layer 402 can be characterized by an effectivedielectric function that is an average of the dielectric functions ofair or gas and the metal layer. For a more detailed description of theeffective medium theory, refer to Choy, “EFFECTIVE MEDIUM THEORY:PRINCIPLES AND APPLICATIONS”, Oxford University Press, 1999, which isincorporated herein by reference in its entirety. The homogenouseffective medium characterization of a structure shall hereinafter bereferred to as an approximation model and the model that includes theirregularities of the inhomogeneous layer or layers of the structureshall be referred to as the fine model.

FIGS. 4A, 4B, 5A, 5B, and 5C are figures to show two examples of patterngeometries amenable to the application of effective medium theory. FIG.4A shows an exemplary architectural diagram of an approximation model430 depicting an unpatterned film stack on a substrate. Theapproximation model 430 comprises three thin film layers 432, 434, and436 on top of the substrate 438. FIG. 4B shows an exemplaryarchitectural diagram of a fine model 440 comprising a patternedstructure in the top thin film layer 432 of fine model 440. The top thinfilm layer 432 is patterned into a repeating structure of lines andspaces with no changes to the second and third layer, 434 and 436, andthe substrate 438.

FIG. 5A is an exemplary architectural diagram of an approximation model500 comprising a stack of thin film layers 510, 512, and 514 on thesubstrate 516. FIG. 5B is an exemplary side-view architectural diagramof a structure 520 comprising a stack of thin film layers 510, 512, and514, with contact holes 518 formed in them (shown as dotted lines). FIG.5C is an exemplary top-view architectural diagram depicting thetwo-dimensional repeating contact hole structure 520 comprising the topthin film layer 510 and repeating contact holes 518 in the unit cells530, 532, 534, and 536. The unpatterned stack of thin film layers 510,512, 514, and the substrate 516, all of structure 500 shown in FIG. 5A,represent the approximation model of structure 520. The repeatingcontact holes 518 extending through the thin film layers 510, 512, and514 of FIG. 5B comprise the fine model for the two-dimension repeatingcontact hole structure. References to a model without qualification meanthe same as a profile model. References to an approximation diffractionmodel include the profile model that is used as an approximation of thestructure and the approximation algorithm used to calculate thesimulated approximation diffraction signal.

FIG. 6A is an exemplary chart of a simulated fine diffraction signal 640using a fine model versus a simulated approximation diffraction signal650 using an approximation model of the structure. As mentioned above,the fine model of the structure may be one-dimensional repeatingstructure, such as a grating, or lines and spaces, or other features, ora repeating two-dimensional structure comprising posts, contact holes,or vias. The simulated fine diffraction signal 640 is generated using anumerical analysis technique such as RCWA, the finite difference method,Green Functions, modal analysis, or the like. For a detailed descriptionof generating a simulated diffraction signal using RCWA, see U.S. Pat.No. 6,891,626, titled CACHING OF INTRA-LAYER CALCULATIONS FOR RAPIDRIGOROUS COUPLED-WAVE ANALYSES, filed on Jan. 25, 2001, issued May 10,2005, which is incorporated herein by reference in its entirety. Thesimulated approximation diffraction signal 650 is based on anapproximation model of the structure, such as an unpatterned stack ofthin films 430 depicted in FIG. 4A for a grating or the unpatternedstack of thin films 500 depicted in FIG. 5A for a repeating structurecomprising contact holes. Referring to FIG. 6A, the difference betweenthe simulated approximation diffraction signal 650 and the simulateddiffraction signal 640 is caused by the presence of the structure, whichcan be lines and spaces in a grating, or the two-dimensional structuressuch as contact holes or other repeating structures. FIG. 6B is anexemplary chart depicting the difference diffraction signal 660calculated by subtracting the simulated approximation diffraction signal650 from the simulated fine diffraction signal 640.

FIG. 7A is an exemplary flowchart for determining profile parametersutilizing approximation and fine diffraction models. In step 702, themetrology model of the structure is developed. The metrology modelcomprises a profile model of the structure, the diffraction model ormodels used to calculate simulated diffraction signals, the type andsettings of the optical metrology tool used. The profile model typicallyincludes a characterization of the shape and layers of the patternedstructure and the number and types of film layers above and/or below thestructure. As mentioned above, one calculation of simulated finediffraction signals involves calculations that utilize the formalism,such as RCWA, related to a solution of Maxwell's electromagneticequations of diffraction. The optical metrology tool is characterized inthe metrology model in terms of whether the tool is a reflectometer, apolarized reflectometer, or an ellipsometer, in the form of technicalspecifications necessary for simulation of the diffraction signal. Theapproximation diffraction model characterizes the structure as amacroscopically homogenous effective medium where the optical propertiescan be described by an effective dielectric function. One example for anapproximation diffraction model is to characterize a patterned structureas a series of thin film layers of material. Referring to FIG. 7A, instep 704, the fine metrology model of the structure is optimized,generating an optimized fine profile model. For a detailed descriptionof optical model optimization, refer to U.S. patent application Ser. No.10/206,291, OPTIMIZED MODEL AND PARAMETER SELECTION FOR OPTICALMETROLOGY, by Vuong, et al., filed on Jun. 27, 2002, which isincorporated in its entirety herein by reference.

In step 706 of FIG. 7A, a set of simulated fine diffraction signals isgenerated using a set of profile parameters of the optimized fineprofile model. The set of profile parameters is generated by using theranges of the profile parameters and the corresponding resolutions ofeach profile parameter. For a detailed description of generation ofsimulated fine diffraction signals using ranges of profile parametersand their corresponding resolutions, refer to U.S. Pat. No. 6,943,900,entitled GENERATION OF A LIBRARY OF PERIODIC GRATING DIFFRACTION SIGNAL,issued on Sep. 13, 2005, which is incorporated herein by reference inits entirety.

Referring to FIG. 7A, in step 708, the simulated approximationdiffraction signal is calculated using an approximation algorithm fordiffraction simulation. An example of an approximation algorithm fordiffraction simulation is the effective medium theory (EMT). Otherexamples of approximation algorithms for diffraction simulation includecoherent potential approximation, random phase approximation, dynamicaleffective medium theory, or the like. For a more detailed description ofother effective medium theory formulations, refer to Choy, “EFFECTIVEMEDIUM THEORY: PRINCIPLES AND APPLICATIONS”, Oxford University Press,1999, and is incorporated in its entirety herein by reference

As mentioned above, an approximation diffraction model characterizes thestructure as a macroscopically homogenous effective medium where theoptical properties can be described by an effective dielectric function.Also mentioned above, one example for an approximation diffraction modelis to characterize a patterned structure as a series of thin film layersof material and characterize the optical properties of the thin filmlayers using the effective dielectric function. In EMT, a periodic orrepeating structure may be replaced by an artificial, anisotropic,homogenous medium if only the zeroth diffraction order propagates withevanescent higher diffraction orders and the grating is sufficientlythick that the incident light does not tunnel through. EMT provides asimple second-order expression in a closed form to give an effectiveindex of a grating or repeating structure in the quasi-static limit, of∇<<<λ, with ∇ and λ being the grating period and free-space wavelengthof the incident light. In mathematical form:

$\begin{matrix}{{ɛ_{{eff},{TE}}^{2} = {ɛ_{0,{TE}} + {\frac{\pi^{2}}{3}{f^{2}\left( {1 - f} \right)}^{2}\left( {ɛ_{A} - ɛ_{B}} \right)^{2}\left( \frac{\Lambda}{\lambda} \right)^{2}}}},} & {1.1{.1}} \\{ɛ_{{eff},{TM}}^{2} = {ɛ_{0,{TM}} + {\frac{\pi^{2}}{3}{f^{2}\left( {1 - f} \right)}^{2}\left( {\frac{1}{ɛ_{A}} - \frac{1}{ɛ_{B}}} \right)^{2}ɛ_{0,{TM}}^{3}{ɛ_{0,{TE}}\left( \frac{\Lambda}{\lambda} \right)}^{2}}}} & {1.1{.2}}\end{matrix}$

where f is the grating volume fill factor, and ∈_(A) and ∈_(B) arerelative permittivities of the grating materials. The zeroth-orderpermittivity ∈₀ in equation 1.1.1 and 1.1.2 is given by:

$\begin{matrix}{ɛ_{0,{TE}} = {{f\; ɛ_{A}} + {\left( {1 - f} \right)ɛ_{B}}}} & {1.1{.3}} \\{ɛ_{0,{TM}} = {\frac{ɛ_{A}ɛ_{B}}{{f\; ɛ_{B}} + {\left( {1 - f} \right)ɛ_{A}}}.}} & {1.1{.4}}\end{matrix}$

For a more detailed description of the calculation of simulatedapproximation diffraction signal using EMT and variations of EMT, referto Moon, et al., “FITTING-BASED DETERMINATION OF AN EFFECTIVE MEDIUM OFA METALLIC PERIODIC STRUCTURE AND APPLICATION TO PHOTONIC CRYSTALS”,Vol. 23, No. 1, January 2006, J. Opt. Soc. of America, which isincorporated in its entirety herein by reference. It is understood thatmany variations and adaptations of the basic equations above areapplicable and may be used in the methods and systems describedherewith.

In step 710, the difference diffraction signal is calculated bysubtracting the simulated approximation diffraction signal from thesimulated fine diffraction signal. In step 712, a best match to ameasured diffraction signal scattered off of the structure is determinedusing a library of difference diffraction signals and the calculatedapproximation diffraction signal The library of difference diffractionsignals may be created from the set of simulated difference diffractionsignals and their corresponding profile model parameters selected insteps 702-710. The calculated approximation diffraction signal issubtracted from the measured diffraction signal and the resultingadjusted measured diffraction signal is matched against the library toget a best match. Alternatively, in step 714, the profile parameterscorresponding to a measured diffraction signal may be determined using amachine learning systems (MLS) trained with the sets of simulateddifference diffraction signals and their corresponding profileparameters. The MLS is trained to process a difference diffractionsignal as input and generate profile parameters as output. Thecalculated approximation diffraction signal is subtracted from themeasured diffraction signal, resulting in an adjusted measureddiffraction signal, which is input to the trained MLS, generatingprofile parameters as output. For a more detailed description of machinelearning systems, see U.S. patent application Ser. No. 10/608,300,titled OPTICAL METROLOGY OF STRUCTURES FORMED ON SEMICONDUCTOR WAFERSUSING MACHINE LEARNING SYSTEMS, filed on Jun. 27, 2003, which isincorporated herein by reference in its entirety.

Referring to FIG. 7A, in step 716, one or more matching criteria arecompared with calculated matching criteria using the results of step 712or 714. The one or more matching criteria may include a goodness of fit(GOF) of the difference diffraction signal from the library, orgenerated by the MLS versus the adjusted measured diffraction signal.Alternatively, a cost function target between the difference diffractionsignal from the library, or generated by the MLS, versus the adjustedmeasured diffraction signal, may be used. If the one or more matchingcriteria are not met, in step 718, the approximation model and/or theapproximation algorithm are modified. Modification of the approximationmodel may involve, for example, floating the thickness of one or more ofthe layers, or conversely, changing a previously floating thickness to afixed value. Modification of the approximation algorithm to calculatethe approximation diffraction signal comprises the use of a variant ofthe effective medium theory formula, or switching from effective mediumtheory to another approximation theory, such as coherent potentialapproximation, random phase approximation, dynamical effective mediumtheory, or the like. Steps 708, 710, 712 or 714, and 716 are iterateduntil the one or more matching criteria are met.

Still referring to FIG. 7A, if the one or more matching criteria aremet, in step 724, at least one determined profile parameter of thestructure is utilized in subsequent device processing. Profileparameters of the optimized profile model typically include low and highranges of thicknesses; for example, a top CD range may have a low valueof 25 nm and a high value of 40 nm. In step 726, the ranges of profileparameters of the optimized profile are adjusted by limiting orexpanding the range as a result of sensitivity analysis or otherstatistical analysis of the effects of the just-determined profileparameter on the measured diffraction signal. In some cases, a profileparameter may not alter the measured diffraction signal, i.e., themeasured diffraction signal is insensitive to changes of the particularprofile parameter. In this case, the particular profile parameter may beset to a fixed value for subsequent library and MLS processing.Conversely, if the just-determined parameter does alter the measureddiffraction signal significantly, then widening the range of variation,or increasing its resolution may be required. In an alternateembodiment, thicknesses and/or widths of thin film layers may be fixedor floated, or the refractive indices and/or the extinction coefficientsof layers may fixed or floated, based on the sensitivity analysis, orother metrics analyzed. For a more detailed description of sensitivityanalysis and use of goals or metrics, see U.S. patent application Ser.No. 10/946,729, titled OPTICAL METROLOGY MODEL OPTIMIZATION BASED ONGOALS, filed on Sep. 21, 2004, which is incorporated herein by referencein its entirety.

FIG. 7B shows an exemplary flowchart for determining profile parametersutilizing approximation and fine diffraction models using a first and asecond machine learning system. In step 810, a set of simulated finediffraction signals is generated using an optimized fine profile model.In step 814, a simulated approximation diffraction signal is calculated,where the calculation performed is similar to that of step 708 of FIG.7A. Referring to FIG. 7B, in step 818, a set of difference diffractionsignals is calculated by subtracting the simulated approximationdiffraction signal from each simulated fine diffraction signal. In step822, a first MLS is trained with the set of difference diffractionsignals and corresponding profile parameters, the first machine learningsystem being trained to process profile parameters as input and generatea difference diffraction signal as output. In step 826, using the rangesof the profile parameters of the optimized profile model and theresolution of each profile parameter, the first MLS is used to generatedifference diffraction signals corresponding to various combinations ofprofile parameters. The simulated approximation diffraction signalcalculated in step 814 is added to the difference diffraction signal andstored in a library of simulated fine diffraction signals, along withthe profile parameters corresponding to the simulated fine diffractionsignals. In step 830, a second MLS is trained using the generatedlibrary where the second MLS is trained to process simulated or measuredfine diffraction signals as input and generate profile parameters asoutput. In step 834, the second MLS or the generated library are used todetermine profile parameters from measured diffractions signals.

In an alternative embodiment, the second MLS is trained in a differentmanner than described above, i.e., the second MLS is trained to processprofile parameters as input and generate fine diffraction signals asoutput. Trial profile parameters are input to the second MLS to generatea fine diffraction signal that is compared to the measured diffractionsignal. If one or more matching criteria such as GOF and/or costfunction are not met in the comparison, then another set of trialprofile parameters is used and the process is iterated using regressiontechniques to converge to the set of trial profile parameters that meetthe one or more matching criteria.

FIG. 7C is an exemplary flowchart for determining profile parametersutilizing approximation and fine diffraction models using one or moretermination criteria for metrology model optimization. Referring to FIG.7C, in step 850, one or more termination criteria for the diffractionmodel optimization process may be set. An example of a terminationcriterion may be repeatability of the measurements using the optimizeddiffraction model. Other termination criteria include accuracy ofmeasurements compared to the measurements with a reference tool such asa scanning electron microscope (SEM), ranges of precision, criticaldimension uniformity, correlation coefficient, goodness-of-fit, costfunction, throughput, closeness of match of measurements made withdifferent metrology devices, and the like. Closeness of match ofmeasurements made with different metrology devices may include one ormore of the absolute measurement difference, average correlation ratiobetween a metrology system and a reference metrology system, thestandard mean deviation (σ) and its multiples, and the total measurementuncertainty. In step 854, a library of difference diffraction signalsand corresponding profile parameters is generated or an MLS is trainedon pairs of difference diffraction signals and corresponding profileparameters, where the difference diffraction signals are generated usingfine and approximation diffraction models. Generation of the library andthe trained MLS are similar to the methods described in the flowchartsdepicted in FIGS. 7A and 7B.

Referring to FIG. 7C, in step 858, the library or trained MLS is used todetermine profile parameters of the structure using measured diffractionsignals. Use of the library and the trained MLS for determining profileparameters are also described in the description of the flowchartsdepicted in FIGS. 7A and 7B. In step 862, if the calculated one or moretermination criteria does not meet the set one or more terminationcriteria, then in step 864 the approximation model is modified and/orthe approximation algorithm is modified. For example, if the settermination criterion is accuracy of the measurement compared tomeasurement of the structure using a SEM, and assuming that theapproximation model used is a structure of fixed thickness and widththin film layers, this model may then be modified by, for example,floating the thickness of one or more of the film layers. Alternatively,if the approximation algorithm used the effective medium theoryequations, the approximation algorithm may be modified to use avariation of the medium theory equations or switch to coherent potentialapproximation, random phase approximation, or dynamical effective mediumtheory. It is understood that other approximation models may be used,such as variations of EMT where of the layer properties are fixed orfloated, or where the refractive indices and/or the extinctioncoefficients of a layers are fixed or floated. The variations of theapproximation model can be matched with other approximation algorithmsmentioned above, or the like.

FIG. 8 is an exemplary block diagram of a system for utilizing a librarydeveloped for determining the profile parameters of a structure usingapproximation and fine diffraction models. In one exemplary embodiment,optical metrology system 904 can also include a library 910 with aplurality of simulated difference diffraction signals and a plurality ofprofile parameters associated with the plurality of simulated differencediffraction signals. As described above, the library 910 can begenerated in advance. Metrology processor 908 can calculate a simulatedapproximation diffraction signal and can compare a measured diffractionsignal off of a structure fabricated in fabrication cluster 902,adjusted by subtracting the simulated approximation diffraction signal,to the plurality of simulated difference diffraction signals in thelibrary When a matching simulated difference diffraction signal isfound, the profile parameters associated with the matching simulateddifference diffraction signal in the library are assumed to correspondto the profile parameters of the actual structure measured by themetrology tool 906.

FIG. 9 is an exemplary block diagram of a system for utilizing a machinelearning system developed for determining the profile parameters of astructure using approximation and fine diffraction models. System 1100includes a fabrication cluster 1102 and an optical metrology system1104. Fabrication cluster 1102 is configured to perform wafer processingto fabricate a structure on a wafer. Optical metrology system 1104includes an optical metrology tool 1106, a processor 1108, and a machinelearning system 1110. Optical metrology tool 1106 can comprisecomponents of a scatterometry device, such as a reflectometer,ellipsometer, and the like. The optical metrology tool 1106 isconfigured to measure a set of diffraction signals off of the structure.Processor 1108 is configured to calculate a simulated approximationdiffraction signal, and is also configured to train machine learningsystem 1110 using the set of measured diffraction signals as inputs, andprofile parameters as the expected outputs of machine learning system1110.

After machine learning system 1110 has been trained, optical metrologysystem 1100 can be used to determine one or more values of one or moreprofile parameters of a structure on the wafer. In particular, astructure is fabricated using fabrication cluster 1102 or anotherfabrication cluster. A diffraction signal is measured off of thestructure using optical metrology tool 1106. The measured diffractionsignal, adjusted by subtracting the simulated approximation diffractionsignal, is input into the trained machine learning system 1110 to obtainone or more values of profile parameters as an output. In one exemplaryembodiment, machine learning system 1110 comprises two machine learningsystems trained and utilized as specified in the method described inconnection with FIG. 7C.

FIG. 10 is an exemplary flowchart for determining and utilizing profileparameters using approximation and fine diffraction models for automatedprocess and equipment control. In step 1210, a library and/or trainedMLS using fine and approximation diffraction models are developed, asdescribed above. In step 1212, at least one profile parameter of astructure is determined using the library or the trained MLS. In step1214, the at least one profile parameter is transmitted to a fabricationcluster configured to perform a processing step, where the processingstep may be executed in the semiconductor manufacturing process floweither before or after measurement step 1212 is made. In step 1216, theat least one transmitted profile parameter is used to modify a processvariable or equipment setting for the processing step performed by thefabrication cluster.

FIG. 11 is an exemplary block diagram of a system for determining andutilizing profile parameters for automated process and equipmentcontrol. System 1400 includes a first fabrication cluster 1402 andoptical metrology system 1404. System 1400 also includes a secondfabrication cluster 1406. Although the second fabrication cluster 1406is depicted in FIG. 11 as being subsequent to first fabrication cluster1402, it should be recognized that second fabrication cluster 1406 canbe located prior to first fabrication cluster 1402 in system 1400 (e.g.and in the manufacturing process flow).

A photolithographic process, such as exposing and/or developing aphotoresist layer applied to a wafer, can be performed using firstfabrication cluster 1402. Optical metrology system 1404 is similar tooptical metrology system 40 of FIG. 1A. In one exemplary embodiment,optical metrology system 1404 includes an optical metrology tool 1408and processor 1410. Optical metrology tool 1408 is configured to measurea diffraction signal off of the structure. Processor 1410 is configuredto compare the measured diffraction signal, adjusted by subtracting thesimulated approximation diffraction signal, to a difference diffractionsignal. The difference diffraction signal was generated usingapproximation and fine diffraction models as described above. If themeasured diffraction signal, adjusted by the simulated approximationdiffraction signal, and the stored difference diffraction signal match,one or more values of the profile parameters are determined to be theone or more values of the profile parameters associated with the storeddifference diffraction signal.

In one exemplary embodiment, optical metrology system 1404 can alsoinclude a library 1412 with a plurality of simulated fine diffractionsignals and a plurality of values of one or more profile parametersassociated with the plurality of simulated fine diffraction signals. Asdescribed above, the library can be generated in advance; metrologyprocessor 1410 can compare a measured diffraction signal off a structureto the plurality of simulated fine diffraction signals in the library.When a matching simulated fine diffraction signal is found, the one ormore values of the profile parameters associated with the matchingsimulated fine diffraction signal in the library is assumed to be theone or more values of the profile parameters used in the waferapplication to fabricate the structure.

System 1400 also includes a metrology processor 1416. In one exemplaryembodiment, processor 1410 can transmit the one or more values of theone or more profile parameters to metrology processor 1416. Metrologyprocessor 1416 can then adjust one or more process parameters orequipment settings of first fabrication cluster 1402 based on the one ormore values of the one or more profile parameters determined usingoptical metrology system 1404. Metrology processor 1416 can also adjustone or more process parameters or equipment settings of the secondfabrication cluster 1406 based on the one or more values of the one ormore profile parameters determined using optical metrology system 1404.As noted above, fabrication cluster 1406 can process the wafer before orafter fabrication cluster 1402. In another exemplary embodiment,processor 1410 is configured to train machine learning system 1414 usingthe set of measured diffraction signals as inputs to machine learningsystem 1414 and profile parameters as the expected outputs of machinelearning system 1414. In one exemplary embodiment, machine learningsystem 1414 comprises two machine learning systems trained and utilizedas specified in the method described in connection with FIG. 7C.

Furthermore, a computer readable medium (not shown) such as computermemory, disk, and/or storage may be used to store the instructions andcomputer programs to determine one or more profile parameters of astructure using an optical metrology model, the optical metrology modelcomprising a profile model, an approximation diffraction model, and afine diffraction model, the difference diffraction signal andcorresponding profile parameters stored in a library. Anotherembodiment, similar computer-executable instructions may be stored in acomputer readable medium such as computer memory, disk, and/or storageto determine one or more profile parameters of a structure using asimilar optical metrology model and using the difference diffractionsignal and corresponding profile parameters in training an MLS. In yetanother embodiment, similar computer-executable instructions may bestored in a computer readable medium such as computer memory, disk,and/or storage to control a photolithography cluster or otherfabrication cluster using determined one or more profile parametersusing the aforementioned methods to control a fabrication cluster.

Although exemplary embodiments have been described, variousmodifications can be made without departing from the spirit and/or scopeof the present invention. Therefore, the present invention should not beconstrued as being limited to the specific forms shown in the drawingsand described above.

1. A method of determining one or more profile parameters of a structureusing an optical metrology model, the optical metrology model comprisinga profile model, an approximation diffraction model, and a finediffraction model, the method comprising: (a) developing a metrologymodel of a structure, the metrology model including a profile model, theprofile model having profile parameters; (b) optimizing the metrologymodel, the optimized metrology model including an optimized profilemodel, (c) calculating a simulated approximation diffraction signalbased on the approximation diffraction model of the structure; (d)generating a set of simulated fine diffraction signals from a set ofprofile parameters, the simulated fine diffraction signals generatedusing the optimized profile model of the structure; (d) calculating aset of difference diffraction signals by subtracting the simulatedapproximation diffraction signal from each of the simulated finediffraction signals of the set of simulated fine diffraction signals andpairing each difference diffraction signal with the correspondingprofile parameters; (e) training a machine learning system using thepairs of difference diffraction signal and corresponding profileparameters, the machine learning system trained to process thedifference diffraction signal as input and generate the profileparameters as output; (f) subtracting the simulated diffraction signalfrom a measured diffraction signal resulting in an adjusted measureddiffraction signal; (g) using the trained machine learning system,inputting the adjusted measured diffraction signal and generatingprofile parameters; and (h) if one or more matching criteria are met,accessing at least one generated profile parameter.
 2. The method ofclaim 1 wherein the structure is a wafer structure.
 3. The method ofclaim 2 wherein the wafer structure is a grating or a repeatingstructure.
 4. The method of claim 1 wherein calculating the simulatedapproximation diffraction signal utilizes an approximation algorithm forthe diffraction simulation.
 5. The method of claim 4 wherein theapproximation algorithm for diffraction simulation uses effective mediumtheory.
 6. The method of claim 5 wherein the effective medium theoryreplaces a periodic structure or a repeating structure with ananisotropic homogenous medium with an effective permittivity.
 7. Themethod of claim 4 wherein approximation algorithm for diffractionsimulation uses coherent potential approximation, random phaseapproximation or dynamical effective medium theory.
 8. The method ofclaim 1 wherein generating the set of simulated fine diffraction signalsis performed using rigorous coupled-wave analysis, finite-difference,Green Function, or modal analysis.
 9. The method of claim 1 furthercomprising: (i) modifying the approximation diffraction model and/orapproximation algorithm; (j) iterating steps (c) through (h) until theone or more matching criteria are met.
 10. The method of claim 9 whereinmodifying the approximation diffraction model and/or the approximationalgorithm comprises modifying an approximation algorithm for diffractionsimulation or switching from using effective medium theory to coherentpotential approximation.
 11. A system for determining one or moreprofile parameters of a structure using optical metrology and simulateddiffraction signals generated using a fine diffraction model and anapproximation diffraction model of a structure having a profile, theprofile having profile parameters, the system comprising: an opticalmetrology tool configured to illuminate the structure with anillumination beam and detect the diffraction signal off the structure; aprocessor configured to generate a simulated approximation diffractionsignal off the structure based on an approximation diffraction model ofthe structure and an approximation algorithm for diffraction simulation,generate a simulated fine diffraction signal off the structure based ona fine diffraction model of the structure and a set of structure profileparameters, and calculate a difference diffraction signal by subtractingthe simulated approximation diffraction signal from the simulated finediffraction signal; and a machine learning system trained with pairs ofdifference diffraction signal and corresponding profile parameters andconfigured to process a difference diffraction signal as input andgenerate profile parameters as output; wherein the structure is measuredby the optical metrology tool generating a measured diffraction signal,the simulated approximation diffraction signal is subtracted from themeasured diffraction signal generating an adjusted measured diffractionsignal, the adjusted measured diffraction signal is input in the trainedmachine learning system, and the trained machine learning systemgenerates profile parameters as output.
 12. The system of claim 11wherein the structure is a grating or a repeating structure.
 13. Thesystem of claim 11 wherein the simulated approximation diffractionsignal is calculated utilizing an approximation algorithm fordiffraction simulation.
 14. The system of claim 13 wherein theapproximation algorithm for diffraction simulation uses the effectivemedium theory.
 15. The system of claim 13 wherein the approximationalgorithm for diffraction simulation uses coherent potentialapproximation, random phase approximation or dynamical effective mediumtheory.
 16. A system for determining one or more profile parameters of astructure using optical metrology and simulated diffraction signalsgenerated using a fine diffraction model and an approximationdiffraction model of a structure having a profile, the profile havingprofile parameters, the system comprising: an optical metrology toolconfigured to illuminate the structure with an illumination beam anddetect the diffraction signal off the structure; a processor configuredto generate a simulated approximation diffraction signal based on anapproximation diffraction model of the structure and approximationalgorithm for diffraction simulation, generate a set of simulated finediffraction signal based on a fine diffraction model of the structureand a set of structure profile parameters, and calculate a set ofdifference diffraction signal by subtracting the approximationdiffraction signal from each simulated fine diffraction signal of theset of simulated fine diffraction signal and pairing the differencesignal with the corresponding profile parameters; a first machinelearning system trained with the pairs of difference diffraction signaland corresponding profile parameters and configured to process profileparameters as input and generate difference diffraction signal asoutput; a library configured to store pairs of profile parameters andassociated simulated fine diffraction signals; a second machine learningsystem trained with the pairs of profile parameters and associatedsimulated fine diffraction signals from the library and configured toprocess measured diffraction signals as input and generate profileparameters as output; wherein the processor creates a set of pairs ofdifference diffraction signals and corresponding profile parameters,trains the first machine learning system with the set of pairs ofdifference diffraction signals and corresponding profile parameters asinput and generate difference diffraction signal as output, generates alibrary of pairs of simulated fine diffraction signals and correspondingprofile parameters, and trains the second machine learning systems usingthe library and process measured diffraction signals as input andgenerate profile parameters as output; and wherein the structure ismeasured by the optical metrology tool generating a measured diffractionsignal, the measured diffraction signal is input to the second machinelearning system, and second machine learning system generates at leastone profile parameter as output.
 17. The system of claim 16 wherein thesimulated approximation diffraction signal is calculated utilizing anapproximation algorithm for diffraction simulation and wherein theapproximation algorithm for diffraction simulation use effective mediumtheory, coherent potential approximation, random phase approximation ordynamical effective medium theory.
 18. A method of determining one ormore profile parameters of a structure using an optical metrology model,the optical metrology model comprising a profile model, an approximationdiffraction model, and a fine diffraction model, the method comprising:generating a set of simulated fine diffraction signals from a set ofprofile parameters using a fine diffraction model; calculating asimulated approximation diffraction signal based on an approximationdiffraction model of the structure; calculating a set of differencediffraction signals by subtracting the simulated approximationdiffraction signal from each simulated fine diffraction signal of theset of simulated fine diffraction signals; training a first machinelearning system with the set of difference diffraction signals andcorresponding profile parameters, the first machine learning systemtrained to process profile parameters as input and generate a differencediffraction signal as output; generating a library of simulated finediffraction signals and profile parameters using the trained firstmachine learning system and using ranges and corresponding resolutionsof the profile parameters; training a second machine learning systemsusing the generated library, the second machine learning systems trainedto process measured diffraction signals as input and generate profileparameters as output; and determining at least one profile parameterfrom a measured diffraction signal using the generated library or thetrained second machine learning system.
 19. A computer-readable storagemedium containing computer-executable instructions to a method fordetermining one or more profile parameters of a structure using opticalmetrology, comprising instructions for: (a) developing a metrology modelof a structure, the metrology model including a profile model, theprofile model having profile parameters; (b) optimizing the metrologymodel, the optimized metrology model including an optimized profilemodel, (c) calculating a simulated approximation diffraction signalbased on an approximation diffraction model of the structure; (d)generating a set of simulated fine diffraction signals from a set ofprofile parameters, the simulated fine diffraction signals generatedusing the optimized profile model of the structure; (d) calculating aset of difference diffraction signal by subtracting the simulatedapproximation diffraction signal from each of the simulated finediffraction signals of the set of simulated fine diffraction signals andpairing each difference diffraction signal with the correspondingprofile parameters; (e) training a machine learning system using thepairs of difference diffraction signal and corresponding profileparameters, the machine learning system trained to process thedifference diffraction signal as input and generate the profileparameters as output; (f) subtracting the simulated diffraction signalfrom a measured diffraction signal resulting in an adjusted measureddiffraction signal; (g) using the trained machine learning system,inputting the adjusted measured diffraction signal and generatingprofile parameters; and (h) if one or more matching criteria are met,accessing at least one generated profile parameter.
 20. Acomputer-readable storage medium containing computer-executableinstructions to a method for determining one or more profile parametersof a structure using optical metrology, comprising instructions for:generating a set of simulated fine diffraction signals from a set ofprofile parameters using a fine diffraction model; calculating asimulated approximation diffraction signal based on an approximationdiffraction model of the structure; calculating a set of differencediffraction signals by subtracting the simulated approximationdiffraction signal from each simulated fine diffraction signal of theset of simulated fine diffraction signals; training a first machinelearning system with the set of difference diffraction signals andcorresponding profile parameters, the first machine learning systemtrained to process profile parameters as input and generate a differencediffraction signal as output; generating a library of simulated finediffraction signals and profile parameters using the trained firstmachine learning system and using ranges and corresponding resolutionsof the profile parameters; training a second machine learning systemsusing the generated library, the second machine learning systems trainedto process measured diffraction signals as input and generate profileparameters as output; and determining at least one profile parameterfrom a measured diffraction signal using the generated library or thetrained second machine learning system.